SPS SPS FM Pure 2024 February — Question 11

Exam BoardSPS
ModuleSPS FM Pure (SPS FM Pure)
Year2024
SessionFebruary
Topic3x3 Matrices

11. Three planes have equations $$\begin{aligned} ( 4 k + 1 ) x - 3 y + ( k - 5 ) z & = 3
( k - 1 ) x + ( 3 - k ) y + 2 z & = 1
7 x - 3 y + 4 z & = 2 \end{aligned}$$
  1. The planes do not meet at a unique point. Show that \(k = 4.5\) is one possible value of \(k\), and find the other possible value of \(k\).
  2. For each value of \(k\) found in part (a), identify the configuration of the given planes. In each case fully justify your answer, stating whether or not the equations of the planes form a consistent system.
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